Unified Theory of Relaxations in Plasmas. III. Quantum Effects

Abstract

The connection formula given in Part I, which unifies the impact and wave theories, is generalized so as to make quantum mechanical calculation possible. A relaxation rate X is given in the form
X=X_κ+X_wave−X_wave,κ.
Here X_wave is the quantity calculated in the wave theory; X_wave,κ is the quantity to which X_wave is reduced when the dielectric permeability is replaced by 1+κ²⁄k², which depends on the wave number k only; X_κ is the quantity calculated in the collision theory with use of the screened Coulomb potential of the form e^−κr⁄r; and κ⁻¹ is any length considerably longer than the close impact radius. The final result is independent of κ. Applications are given.